diff --git a/PIL/TiffImagePlugin.py b/PIL/TiffImagePlugin.py
index a84d01755..7b23df392 100644
--- a/PIL/TiffImagePlugin.py
+++ b/PIL/TiffImagePlugin.py
@@ -208,6 +208,8 @@ OPEN_INFO = {
 
 PREFIXES = [b"MM\000\052", b"II\052\000", b"II\xBC\000"]
 
+FLOAT_MIN = sys.float_info.min * sys.float_info.epsilon
+
 
 def _accept(prefix):
     return prefix[:4] in PREFIXES
@@ -477,7 +479,7 @@ class ImageFileDirectory_v2(collections.MutableMapping):
     @_register_loader(5, 8)
     def load_rational(self, data, legacy_api=True):
         vals = self._unpack("{0}L".format(len(data) // 4), data)
-        combine = lambda a, b: (a, b) if legacy_api else a / b
+        combine = lambda a, b: (a, b) if legacy_api else a / (b or FLOAT_MIN)
         return tuple(combine(num, denom)
                      for num, denom in zip(vals[::2], vals[1::2]))
 
diff --git a/Tests/images/exif_zerodivisionerror.jpg b/Tests/images/exif_zerodivisionerror.jpg
new file mode 100644
index 000000000..2715215a2
Binary files /dev/null and b/Tests/images/exif_zerodivisionerror.jpg differ
diff --git a/Tests/test_file_jpeg.py b/Tests/test_file_jpeg.py
index 367e57c14..a4949d4d7 100644
--- a/Tests/test_file_jpeg.py
+++ b/Tests/test_file_jpeg.py
@@ -177,6 +177,12 @@ class TestFileJpeg(PillowTestCase):
         # Should not raise a TypeError
         im._getexif()
 
+    def test_exif_zerodivisionerror(self):
+        im = Image.open('Tests/images/exif_zerodivisionerror.jpg')
+
+        # Should not raise a ZeroDivisionError
+        im._getexif()
+
     def test_progressive_compat(self):
         im1 = self.roundtrip(hopper())
         im2 = self.roundtrip(hopper(), progressive=1)